Every uncountable abelian group admits a nonnormal group topology
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- by F. Javier Trigos-Arrieta PDF
- Proc. Amer. Math. Soc. 122 (1994), 907-909 Request permission
Abstract:
If G is a locally compact Abelian group, let ${{\mathbf {G}}^ + }$ denote the underlying group of G equipped with the weakest topology that makes all the continuous characters of G continuous. Thus defined, ${{\mathbf {G}}^ + }$ is a totally bounded topological group. We prove: Theorem. ${{\mathbf {G}}^ + }$ is normal if and only if G is $\sigma$-compact. When G is discrete, this theorem answers in the negative a question posed in 1990 by E. van Douwen, and it partially solves a problem posed in 1945 by A. Markov.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 907-909
- MSC: Primary 22B05; Secondary 54A10, 54A25, 54H11
- DOI: https://doi.org/10.1090/S0002-9939-1994-1209100-7
- MathSciNet review: 1209100